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Maths Development Team: Lesson Study 2017-2018

Lesson Research Proposal

For the lesson 17/01/18 At St.Colmans Community College, Midleton,

Teacher’s name: Michael Barrett Class: Rang Fergal

Instructor: Enda O Connell Lesson plan developed by: Anne O’Connor, Margaret O’Connell, Sarah Fitzpatrick, Michael Barrett

1. Title of the Lesson: Subway Substitution

2. Brief description of the lesson Students will be introduced to the chapter of Algebra. Students will recap over key words such as variable, term, Constant, coefficient and Expression. They will be able to derive an expression off a menu. They will then be able to substitute values into the given expression. Research Theme

Ø Learner Experiences

(a.) We hope that students get a great sense of enjoyment out of meaningful learning.

(b.) We aim for students to challenge and support one another in their learning interactions.

(c.) We will strive for students to reflect on their learning throughout.

Ø Teachers Collective/ Collaborative Approach

(a.) We, as teachers, hope to enhance the range of teaching methodologies that we can use in

the day to day classroom.

(b.) Working together will allow us to partake in professional collaboration with our

colleagues.

(c.) Collaboration will then allow us to devise learning opportunities to meet the varying

needs present in the classroom.


3. Background & Rationale a) Why did we choose algebra as a research topic?

We at St.Colmans Community College, Midleton have identified Algebra as a problem area

amongst our students. Common problems include trying to relate Algebra to their everyday life.

Problems also arise when trying to relate their knowledge in Algebra to other topics present in the

Mathematics curriculum.

b) Our Research findings:

When looking at the 2015 ordinary level junior cert results we noticed that when algebra was put

with a secondary topic the mean results were quiet high. In contrast, when algebra was examined as

a singular question, the mean results were considerably lower. (SEE APPX 1) On future discussion,

we felt that the rote learning approach around algebra wasn’t working effectively. Students weren’t

retaining the steps required to complete the algebraic questions correctly. When algebra is put with a

secondary topic, for example- distance, speed and time, students feel better equipped to answer the

question. We put this down to teaching approaches such as the use of imagery, graphs and

estimation techniques.

4. Relationship of the Unit to the Syllabus

Related prior learning Outcomes

Learning outcomes for this unit

Related later learning outcomes

• number sentences with a frame into word problems and vice versa

• word problems with a variable into number sentences

• Solve one-step number sentences and equations

• Explore the concept of a variable in the context of simple patterns, tables and simple formulae and substitute values for

• Generating arithmetic expressions from repeating patterns

• Representing situations with tables, diagrams and graphs

• Expressions

• Finding formulae Examining algebraic relationships

• Using graphs to represent phenomena quantitatively.

• Equations and

• Generating arithmetic expressions from repeating patterns

• Representing situations with tables, diagrams and graphs

• Expressions

• Finding formulae Examining algebraic relationships

• Using graphs to represent phenomena quantitatively.

• Equations and


variables inequalities

inequalities

• Expressions

5. Goals of the Unit • Evaluate Algebraic expressions. • Add and Subtract algebraic terms. • Multiply algebraic expressions. • Multiply algebraic terms. • Students will develop problem solving skills and appreciate that there are multiple

approaches to problem solving. • Students will gain the value and respect of each other’s work.

6. Unit Plan

Lesson Learning goal(s) and tasks 1

Introduction to algebra – Evaluating Algebraic Expressions (x2) Research Lesson

2 Adding and Subtracting like terms (x1) Multiplication of terms (x2) 4 Multiplication of brackets (x2) 5 Multiplication of two expressions (x2)

6 Revision and assessment (x2)


7. Goals of the Research Lesson: • Recap over key words – Expression, Coefficient, Term, Constant, Variable. • Derive Algebraic expressions. • Substitute different values into the given algebraic expressions.

a) Key Skills and Statements of Learning

• Students will develop problem solving skills. • Students will be able to derive expressions. • Students will be able to evaluate given expressions.

8. Flow of the Research Lesson: TITLE: Subway’s Substitution

Steps, Learning Activities Teacher’s Questions and Expected Student Reactions

Teacher Support Assessment

The pupils are welcomed, a roll call is taken, and the guidelines for this class are re-enforced. (3 mins)

The seating plan for the class will allow for students to be in groups of three. Each group will be given a plastic pocket full of resources for the class.

Introduction Prior knowledge on key words of Algebra will be discussed. Pupils are reminded to be mindful that a variable can always be different. Pupils are asked to have their hardbacks, calculators and a pen on their desk. (4 mins)

I will refer students to the word wall to identify all of the different meanings of the key word. (Variable, term, algebraic expression, substitution, co-efficient).

I will orally examine students on the words.

Task 1: (1.) I will introduce the task on the PowerPoint. We will collaboratively examine the menu. I will then assign students to outline the different ways in which they could spend the €15. (6 mins)

Working individually in their groups students will compile their different ways of spending the €15. (2 – 4 mins) Solutions will then be discussed within the group. (2 mins)

I will circulate around the room assessing that each student is participating in the group work and examine the different ways in which they are spending the €15.


(2.) Review – A member of selected groups will present a way of spending the €15 on the whiteboard. (6 mins)

Each of the identified groups will have a separate part of the whiteboard to write out their nominated solution.

I will identify certain solutions that will be presented on the whiteboard.

Task 2: Students will rejoin their groups again. Using their three different solutions from task 1 above, groups will have to write a simplified expression for their three solutions. Review – I will select a member from the class to come to the whiteboard to write a simplified version of an equation that was presented on the whiteboard from task 1. (5 mins)

A member in each group will pick a particular way of spending the €15 and write a simplified expression. I will generate a discussion on how students simplified their expressions.

I will move around the room again to ensure that each student is writing a simplified expression. Assessing the solutions on the whiteboard.

Task 3: I will pose task three to the class. In task three students will have to prove that their order is equivalent to €15. I will remind students of what a variable is and how it may vary. Review – A member from each group will be brought to the whiteboard for the final time to

Students will have to refer back to the menu to find the different values for the different options. They will ensure that the three selected options add up to €15. Selected students will present their calculations on the whiteboard.

I will ensure that students in each group are substituting values into one of the groups chosen expressions. I will ensure that each expression adds up to €15.


ensure that the expressions presented on the whiteboard add up to €15. (8 mins)

Comparing and Discussing: Collaboratively, we will go through the different tasks from the lesson. We will discuss the material presented on the board. As a class we will agree on one notation for the options on the menu. Homework assignment handed out now and students will note their homework in their journals. (4 mins)

Summing up & Reflection: Students will review their learning using the traffic lights system. I.e. how confident they are in writing an expression and filling in values for different expressions. (4 mins)

I will ascertain the students understanding of this topic by using this assessment of learning (AOL) tool. This will provide valuable information for planning tomorrow’s lesson.

NOTES re in-between desk work

• When students are writing their expression on the whiteboard I will highlight any miss-conceptions of the work then. By doing this students get to analysis where they might potentially go wrong.

• I will move around the classroom when students are filling in their expressions. This way I can monitor any mistakes made. If there is a recurring mistake I will highlight it on the whiteboard.

• Throughout the lesson I will ensure that I stick to my time plan.

9. Board Plan


Evaluation: As a group we felt the goals of the lessons were met. The seating plan allowed for group discussion.

Firstly, students worked on the task themselves before discussing the task collaboratively. Students

weren’t afraid to engage with each other throughout the lesson. Students used various approaches such as

the listing method, tabulating, abbreviating the words using variables while displaying their work

vertically and horizontally.

10. Reflection Learner Experiences:

From the post lesson reflection, that the students completed, it was evident that the students thoroughly

enjoyed and engaged in the lesson and could see the everyday relevance of Algebra. Students enjoyed

the opportunity to discuss the different tasks. Each student had a voice. The class took pride in the work

that they displayed. The class appreciated the different approaches taken to the different problems. The

lesson was student lead. Students had control of their own learning by deciding which solution would

be put forward as an agreed solution. As a class they debated the merits of each solution presented and

decided which method they would use going forward, with a clear understanding of why this method

was chosen. The traffic lights system gave an immediate visual demonstration of understanding. This

was further supported in the post lesson reflection. Students had a great sense of respect of each other’s

work. There was a willingness to listen and learn from one another. From a teacher point of view, the

advanced preparation and planning allowed for the lesson to flow easily.


Appendix: Appx 1 (a.)

JUNIOR CERTIFICATE EXAMINATION 2015 MATHEMATICS

CHIEF EXAMINER’S REPORT

Analysis of Candidate Performance Ordinary Level


Appx 1 (b.) Analysis of Candidate Performance Higher Level


Appx 2 (a.)

OL Algebra Questions


Appx 2 (b.)

HL Junior Cert Algebra Questions


ppendix 1


Quality Framework for Post-Primary Schools – Teaching & Learning

Learner outcomes

Students enjoy their learning, are motivated to learn, and expect to achieve as learners

☐

Students have the necessary knowledge and skills to understand themselves and their relationships

☐

Students demonstrate the knowledge, skills and understanding required by the post-primary curriculum

☐

Students attain the stated learning outcome for each subject, course and programme

☐

Learner experiences

Students engage purposefully in meaningful learning activities ☐ Students grow as learners through respectful interactions and experiences that are challenging and supportive

☐

Students reflect on their progress as learners and develop a sense of ownership of and responsibility for their learning

☐

Students experience opportunities to develop the skills and attitudes necessary for lifelong learning

☐

Teachers’ individual practice

The teacher has the requisite subject knowledge, pedagogical knowledge and classroom management skills

☐

The teacher selects and uses planning, preparation and assessment practices that progress students’ learning

☐

The teacher selects and uses teaching approaches appropriate to the learning intention and the students’ learning needs

☐

The teacher responds to individual learning needs and differentiates teaching and learning activities as necessary

☐

Teachers’ collective / collaborative practice

Teachers value and engage in professional development and professional collaboration

☐

Teachers work together to devise learning opportunities for students across and beyond the curriculum

☐

Teachers collectively develop and implement consistent and dependable formative and summative assessment practices

☐

Teachers contribute to building whole-staff capacity by sharing their expertise

☐


Junior Cycle Key Skills and Statements of Learning Key Skills KS1 Managing myself KS2 Staying well KS3 Monitoring information & thinking KS4 Being numerate KS5 Being creative KS6 Working with others KS7 Communicating KS8 Being literate

Statements of Learning The student SL1 communicates effectively using a variety of means in a range of contexts in L1* SL2 listens, speaks, reads and writes in L2* and one other language at a level of proficiency

that is appropriate to her or his ability SL3 creates, appreciates and critically interprets a wide range of texts SL4 creates and presents artistic works and appreciates the process and skills involved SL5 has an awareness of personal values and an understanding of the process of moral

decision making SL6 appreciates and respects how diverse values, beliefs and traditions have contributed to

the communities and culture in which she/he lives SL7 values what it means to be an active citizen, with rights and responsibilities in local

and wider contexts SL8 values local, national and international heritage, understands the importance of the

relationship between past and current events and the forces that drive change SL9 understands the origins and impacts of social, economic, and environmental aspects of

the world around her/him SL10 has the awareness, knowledge, skills, values and motivation to live sustainably SL11 takes action to safeguard and promote her/his wellbeing and that of others SL12 is a confident and competent participant in physical activity and is motivated to be

physically active SL13 understands the importance of food and diet in making healthy lifestyle choices SL14 makes informed financial decisions and develops good consumer skills SL15 recognises the potential uses of mathematical knowledge, skills and understanding in

all areas of learning SL16 describes, illustrates, interprets, predicts and explains patterns and relationships SL17 devises and evaluates strategies for investigating and solving problems using

mathematical knowledge, reasoning and skills SL18 observes and evaluates empirical events and processes and draws valid deductions and

conclusions SL19 values the role and contribution of science and technology to society, and their

personal, social and global importance


SL20 uses appropriate technologies in meeting a design challenge SL21 applies practical skills as she/he develop models and products using a variety of

materials and technologies SL22 takes initiative, is innovative and develops entrepreneurial skills SL23 brings an idea from conception to realisation SL24 uses technology and digital media tools to learn, communicate, work and think

collaboratively and creatively in a responsible and ethical manner *L1 is the language medium of the school (Irish in Irish-medium schools). L2* is the second language (English in Irish-medium schools).

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